Season the chicken thighs on both sides with kosher salt and black pepper.
Heat olive oil in a large deep skillet or Dutch oven over medium-high heat.
Add the chicken thighs skin-side down and cook until the skin is golden brown and crispy, about 5-7 minutes.
Flip the chicken thighs and cook for another 3 minutes. Remove the chicken from the skillet and set aside.
In the same skillet, add the diced onion, carrot, and celery. Cook, stirring occasionally, until the vegetables are softened, about 5 minutes.
Add the minced garlic and cook for 1 minute until fragrant.
Stir in the rinsed rice, coating it well with the vegetables and oil.
Pour in the chicken broth, then add dried thyme and smoked paprika. Stir to combine.
Return the chicken thighs to the skillet, placing them on top of the rice mixture.
Bring the liquid to a boil, then reduce heat to low, cover, and simmer for 25 minutes, or until the rice is tender and the chicken is cooked through.
Remove the lid and sprinkle frozen peas over the rice. Cover again and cook for an additional 5 minutes until peas are heated through.
Remove from heat and let sit covered for 5 minutes.
Sprinkle chopped fresh parsley over the dish before serving.